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The principal reason for high nonlinearity considerations is the non-Markov behavior observed in nonlinear phenomena. Markov processes are frequently assumed in the technical applications while no process in nature is truly Markov. In this paper the symbolic dynamics of super stable periodic orbits generated by the logistic maps are explored. The grammar and its statistical properties that characterize the long-range correlations between the words of symbolic sequences are studied. The analysis and design of a system based on the nonlinear dynamics considerations is the main achievement of the paper. The turbo coding schemes are explored for the transmission of long-range correlated sequences, and the results are observed by modifying the parameters at coder and decoder ends based on the correlation in the sequence.